Valiant introduced the class VNP with respect to "arithmetic circuits" over 35 years ago in a "rough" analogy to NP. Recently, there have been major advances in the area of arithmetic circuits eg as ...

I am quite certain that I am not the first to entertain the idea that I am going to present. However, it would be helpful if I can find any literature related to the idea.
The idea is to construct a ...

I recall Scott Aaronson making the claim that either $P\neq NP$ or he has superpowers.
What reason is there, if any, to believe that it is not the case that any decision procedure has constants (or ...

I've asked a similar question in cs.se, but didn't get a satisfying answer.
Assuming $P\neq NP$, what can we say about the runtime of any algorithm for an $NP$-complete problem?
Obviously, it means ...

the paper "In defense of the Simplex Algorithm's worst-case behavior" Disser/Skutella [1] was recently cited on this tcs.se site by saeed on another interesting question. the paper introduces the idea ...

The famous Isomorphism Conjecture of Berman and Hartmanis says that all $NP$-complete languages are polynomial time isomorphic (p-isomorphic) to each other. The key significance of the conjecture is ...

I want to ask a question concerning some aspects of the P vs. NP problem.
NOTE: Possibly by "popular" standards i am a crank (i tend towards P=NP), but lets focus on the issue (please with a grain of ...

It is well known by Ladner's Theorem that if ${\mathsf P}\neq \mathsf {NP}$, then there exist infinitely many $\mathsf {NP}$-intermediate ($\mathsf{NPI}$) problems. There are also natural candidates ...

I'm not talking about the RSA, El-gamal, nor any specific encryption scheme. Rather, my question, as related to this and this threads, is why the idea of Public-Key encryption scheme cannot be secure ...

This answer to Major unsolved problems in theoretical computer science? question states that it is open if a particular problem in NP requires $\Omega(n^2)$ time.
Looking at the comments under answer ...

We are given a Boolean formula $F$ in conjunctive normal form with $n$ variables and $m$ clauses and we would like to know if there exists at least one assignment to the $n$ variables that makes $F$ ...

I approximately copied the brief "introduction" to average-case complexity theory of NP from my previous question. However, this question is completely different, so please read on
It is conjectured ...

It is conjectured that NP-complete problems are hard not only in the worst case but also in the typical case. Formally, given a language $S \in \lbrace 0,1 \rbrace^*$ and for each $n$ a probability ...

It is conjectured that $\mathsf{NP} \nsubseteq \mathsf{P}/\text{poly}$ since the converse would imply $\mathsf{PH} = \Sigma_2$. Ladner's theorem establishes that if $\mathsf{P} \ne \mathsf{NP}$ then ...

It is my first question on this site. I am taking a master's course on theory of computation. How you would explain P = NP problem to a 10 year old child and why it has such a monetary reward on it?
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I was recently reminded about the $\mathsf{P}$ vs. $\mathsf{NP}$ problem as explained by Stephen A. Cook on Clay Mathematics Institute.
It has piqued my interest and I would like to learn more about ...

According to an article on pseudorandom number generators (PRNG) by Jeff Lagarias, he states that trying to prove that a PRNG is unpredictable (secure) is just "as hard" as trying to prove that P!=NP. ...

The following question uses ideas from cryptography applied to complexity theory. That said, it is a purely complexity-theoretic question, and no crypto knowledge whatsoever is required to answer it.
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